Extremal Numbers of Generalised Face-Incidence Graphs via an Algebraic Reflection-Group Method
An upper bound on the extremal number ex(n,H) - the maximum edge count of an n-vertex graph containing no copy of H - for the family of generalised face-incidence graphs, which includes the face-incidence graphs of regular polytopes. The bound is obtained by recasting the Conlon-Lee reflection-group technique for controlling repeated applications of the Cauchy-Schwarz inequality in a purely algebraic form and combining it with the Janzer-Sudakov percolation criterion; the same algebraic framework also simplifies proofs concerning weakly norming graphs.
On the extremal number of incidence graphs
In extremal graph theory the extremal number ex(n,H) is the largest number of edges in an n-vertex graph that contains no copy of H. This paper proves a general upper bound on ex(n,H) for the family …